Unit 3 Lesson 5 - Graphing Polynomials

Unit 3 Lesson 5 - Graphing Polynomials

PAGE 19 & 20 IN YOUR PACKET

Warm Up - page 19

Fill in page 19 in your notes using the next 4 slides!

Don't forget what our ends will look like depending on our leading coefficient & degree!

Then answer the 3 questions at the end of this section.

LEADING COEFFICIENT:

Positive

DEGREE:

Even

Example:

 $3x^4-4x+1$  

LEADING COEFFICIENT:

Positive

DEGREE:

Odd

Example:
 $2x^3-1$  

LEADING COEFFICIENT:

Negative

DEGREE:

Even

Example:

 $-2x^4+9x+3$  

LEADING COEFFICIENT:

Negative

DEGREE:

Odd

Example:
  $-3x^7-5x^2+x$  

Multiple Choice

Which way will the right arrow point for the following polynomial:

 $-2x^4+3x-1$  

• Up

• Down

Multiple Choice

Which way will the left arrow point for the following polynomial:

 $-2x^4+3x-1$  

• Up

• Down

Multiple Choice

Which of the following graphs is an appropriate sketch of the polynomial:

 $x^3+3x^2-4x$  

End Behavior - page 20

Use the next 9 slides to understand End Behavior & to fill in your notes on page 20

Then answer the 7 questions at the end of this section.

END BEHAVIOR

We use End Behavior to describe the ends of the graphs on each side (where the arrows are pointing!) 

We say it, 

"As x approaches  $\left(\rightarrow\right)$ negative infinity $\left(-\infty\right)$ , 
 $f\left(x\right)\$  approaches  $\left(\rightarrow\right)$  positive infinity OR negative infinity" 
&
"As x approaches  $\left(\rightarrow\right)$  positive infinity $\left(+\infty\right)$ , 
  $f\left(x\right)\$  approaches  $\left(\rightarrow\right)$  positive infinity OR negative infinity" 

LEADING COEFFICIENT:

Positive

DEGREE:

Even

Look at the left arrow, it is going to  $+\infty$  

Look at the right arrow, it is going to  $+\infty$  

We would say this as:

"As x approaches negative infinity, f(x) approaches positive infinity"

and

"As x approaches positive infinity, f(x) approaches positive infinity"

LEADING COEFFICIENT:

Positive

DEGREE:

Odd

Look at the left arrow, it is going to  $-\infty$  
Look at the right arrow, it is going to  $+\infty$  

We would say this as:

"As x approaches negative infinity, f(x) approaches negative infinity"

and

"As x approaches positive infinity, f(x) approaches positive infinity"

LEADING COEFFICIENT:

Negative

DEGREE:

Even

Look at the left arrow, it is going 

to  $-\infty$  
Look at the right arrow, it is going 

to  $-\infty$  

We would say this as:

"As x approaches negative infinity, f(x) approaches negative infinity"

and

"As x approaches positive infinity, f(x) approaches negative infinity"

LEADING COEFFICIENT:

Negative

DEGREE:

Odd

Look at the left arrow, it is going to  $+\infty$  
Look at the right arrow, it is going to  $-\infty$  

We would say this as:

"As x approaches negative infinity, f(x) approaches positive infinity"

and

"As x approaches positive infinity, f(x) approaches negative infinity"

~ For the next questions~

You will need information from pages 9 & 10 in your packet

Multiple Choice

As which root does the graph

 $f\left(x\right)=\left(x-5\right)^3\left(x+2\right)^2$  touch (or bounce off) the x-axis?

• -5

• -2

• 2

• 5

Multiple Choice

At which root does the graph

 $f\left(x\right)=\left(x+4\right)^6\left(x+7\right)^5$  cross the x-axis?

• -7

• -4

• 4

• 7

Multiple Choice

What is the end behavior of the graph of the polynomial function

 $f\left(x\right)=3x^6+30x^5+75x^4$  

Multiple Choice

What is the end behavior of the graph of the polynomial function  $f\left(x\right)=2x^3-26x-24$  

Multiple Choice

Which graph shows the same end behavior as the graph

 $f\left(x\right)=2x^6-2x^2-5$  ?

Multiple Choice

Which function could represent the graph?

• $f\left(x\right)=x\left(x-a\right)^3\left(x-b\right)^3$

• $f\left(x\right)=\left(x-a\right)^2\left(x-b\right)^2$

• $f\left(x\right)=x\left(x-a\right)^6\left(x-b\right)^2$

• $f\left(x\right)=\left(x-a\right)^5\left(x-b\right)$

Multiple Choice

A polynomial function has:

a root of –4 with multiplicity 4,

a root of –1 with multiplicity 3, and

a root of 5 with multiplicity 6.

If the function has a positive leading coefficient and is of odd degree, which could be the graph of the function?

Yay! You're finished!

If you finish early, please work on pages 21 & 22 in your packet